Metal based thermal dissipator having enhanced thermal radiation, and methods for producing the same

ABSTRACT

A composite thermal dissipator and a method for fabricating the same is disclosed. The composite thermal dissipator includes a molded polydimethylsiloxane (PDMS) composite material composed of a powdered metal mixed with PDMS. The method for fabricating a composite thermal dissipator includes mixing a powdered copper into liquid PDMS to form a liquid mixture, and pouring the liquid mixture into a sacrificial wax mold. The sacrificial wax mold includes wax shaped to be complementary to the composite thermal dissipator. The method also includes curing the liquid mixture within the sacrificial wax mold, and removing the composite thermal dissipator from the sacrificial wax mold by melting away the wax.

RELATED APPLICATIONS

This application claims the benefit of U.S. provisional patent application 63/208,405, filed Jun. 8, 2021 titled “Super-Planckian Near-Field Thermal Dissipator and Method for Producing the Same”. This application also claims the benefit of U.S. Provisional Application No. 63/219,820, filed Jul. 8, 2021 titled “Structured Polydimethylsiloxane (PDMS) Composite for Heat Dissipation”. The entirety of the above referenced disclosures are hereby incorporated herein by this reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under FA9550-17-1-0080 awarded by the Air Force Office of Scientific Research. The government has certain rights in the invention.

TECHNICAL FIELD

Aspects of this document relate generally to thermal dissipators.

BACKGROUND

High-performance electronic devices like central processing units (CPUs) and graphics processing units (GPUs) generate intensive heat. If not managed, this heat eventually leads to overheating problems and even system failure. Heat dissipation plays a crucial role in maintaining the reliability of electronic devices. However, along with an increasing demand for greater processing power, the form factors of these devices is becoming smaller and smaller due to the rising demands for mobile and wearable devices, making effective heat dissipation more challenging.

Traditionally, heat sinks have been the most used component for heat dissipation in electronic devices. They work by transferring the heat from the devices to the surrounding fluid medium, usually air or liquid coolants. Many efforts have been made to improve the performance of heat sinks. For example, optimizing the topology of heat sinks into tree-branch shapes significantly increased the Grashof number. Microchannels and nanofluids have been introduced to achieve extremely high heat transfer rates. Phase change materials have been employed in heat sinks as coolant due to their large heat of fusion. Carbon nanotubes have been employed as on-chip cooling fins, exhibiting cooling capacity for very high power density. Furthermore, metal foams offer advantages in thermal dissipation applications because of their low thermal resistance and lightweight properties. Working individually or filled in conventional fins, metal foams significantly enhance heat transfer performance.

Despite all the innovative approaches to improving performance, the working principle of a heat sink consists of two major processes: conducting heat out of the device and dissipating the heat to a medium. The conduction process requires high thermal conductivity of heat sink materials. Therefore, metals like aluminum and copper are commonly employed. The heat dissipation process is generally driven by either forced or natural convection. The nature of convection benefits from a larger surface area in contact with the cooling medium (e.g., air or coolant). As a result, most heat sinks have extended surfaces, or fins, to enhance the convectional heat transfer.

As another fundamental mechanism of heat transfer, thermal radiation is usually neglected when designing heat sinks with forced convection and small temperature difference above ambient conditions. This is because, in such cases, the convection is dominant. However, for natural-convection heat sinks, thermal radiation contributes 25-40% of the total heat transfer. This presents an opportunity for significantly improved heat transfer via radiative enhancement.

As previously mentioned, conducting heat out of a device requires high thermal conductivity. Metals are commonly employed for this reason. However, the thermal emittance of metals is usually very low, resulting in suppressed thermal radiation. Polymer materials, on the other hand, possess high emittance, which is essential for enhancing thermal emission. Furthermore, polymers are usually lightweight and manufacturing-friendly, able to be formed with complicated topologies. Yet despite all these attractive features, polymers are rarely used as heat sink or thermal dissipator materials, due to their low thermal conductivity.

In the context of microelectronics, dealing with unwanted heat is further complicated by size constraints. Modern microelectronics continue to increase in power while also decreasing in size, thanks to advancements in fabrication technologies, materials, and device architectures. As a result, heat dissipation has become a significant bottleneck for microelectronics. An increasing amount of heat needs to be transferred without sacrificing the small size of the device. Previous attempts at solving this problem have not recognized radiation as a viable means for dissipating heat in these devices, mainly due to the limitation of dealing in the far field.

Photon tunneling in the near-field can enhance radiative heat transfer to overcome the blackbody limit governed by Planck's law when the vacuum gap between two radiating media is much less than the characteristic thermal wavelength. Potential applications of near-field radiation (NFR) include, but are not limited to, near-field thermopower generation (e.g., thermophotovoltaics, etc.), noncontact heat control (e.g., thermal rectification, etc.), and radiative refrigeration.

Previous attempts to harness near-field radiation for super-Planckian radiative heat have relied on polar materials, or formed the gap between a microsphere and a surface, greatly limiting the total radiative heat transfer. Achieving nanometer gaps and parallelism across mesoscale lateral size of plate-plate configurations has been a major challenge. Previous methods of creating the vacuum gap include the formation of low-density pillars, a solution that would be expensive and difficult to scale up for implementation outside a laboratory setting.

Some prior efforts to enhance near-field radiation have employed various materials, such as glass and bare silicon. Metals, on the other hand, are much less studied for near-field thermal radiation. Metals are widely used in microelectronics (e.g., electrodes, conducting pads, etc.). Metals are known to have plasma frequencies typically in the ultraviolet to the visible wavelength ranges; therefore, coupled surface plasmon polaritons cannot occur in the infrared for significant near-field enhancement around room temperature. In addition, metals are normally known as bad thermal emitters in the far-field due to their very low emissivity, typically just a few percent.

SUMMARY

According to one aspect, a method for fabricating a composite thermal dissipator includes mixing a powdered copper into liquid polydimethylsiloxane (PDMS) to form a liquid mixture, and pouring the liquid mixture into a sacrificial wax mold. The sacrificial wax mold includes wax shaped to be complementary to the composite thermal dissipator. The method also includes curing the liquid mixture within the sacrificial wax mold, and removing the composite thermal dissipator from the sacrificial wax mold by melting away the wax.

Particular embodiments may comprise one or more of the following features. The method may further include covering the sacrificial wax mold with a substrate such that the substrate may be in contact with the liquid mixture. The composite thermal dissipator may include the substrate. The powdered copper may have a particle size of less than 75 μm. The weight ratio of powdered copper to PDMS may be between 3.7 and 4. The composite thermal dissipator may include a plurality of fins, each fin having a perimeter and a cross-sectional area such that the perimeter-to-cross-sectional-area ratio may be at least 400 m⁻¹.

According to another aspect of the disclosure, a method for fabricating a composite thermal dissipator includes mixing a powdered metal into liquid polydimethylsiloxane (PDMS) to form a liquid mixture, and pouring the liquid mixture into a mold. The mold is shaped to be complementary to the composite thermal dissipator. The method also includes curing the liquid mixture within the mold, and removing the composite thermal dissipator from the mold.

Particular embodiments may comprise one or more of the following features. The mold may be a sacrificial wax mold comprising wax shaped to be complementary to the composite thermal dissipator. Removing the composite thermal dissipator from the mold may include melting away the wax of the sacrificial wax mold. The method may further include covering the mold with a substrate such that the substrate may be in contact with the liquid mixture. The composite thermal dissipator may include the substrate. The powdered metal may be powdered copper. The powdered metal may have a particle size of less than 75 μm. The weight ratio of powdered metal to PDMS may be between 3.7 and 4. The composite thermal dissipator may include a plurality of fins, each fin having a perimeter and a cross-sectional area such that the perimeter-to-cross-sectional-area ratio may be at least 400 m⁻¹. The liquid mixture may be cured within the mold at room temperature.

According to yet another aspect of the disclosure, a composite thermal dissipator includes a molded PDMS composite material composed of a powdered metal mixed with PDMS.

Particular embodiments may comprise one or more of the following features. The composite thermal dissipator may further include a substrate coupled to the molded composite material. The powdered metal may be powdered copper. The powdered metal may have a particle size of less than 75 μm. The weight ratio of powdered metal to PDMS may be between 3.7 and 4. The composite thermal dissipator may further include a plurality of fins, each fin having a perimeter and a cross-sectional area such that the perimeter-to-cross-sectional-area ratio may be at least 400 m⁻¹.

Aspects and applications of the disclosure presented here are described below in the drawings and detailed description. Unless specifically noted, it is intended that the words and phrases in the specification and the claims be given their plain, ordinary, and accustomed meaning to those of ordinary skill in the applicable arts. The inventors are fully aware that they can be their own lexicographers if desired. The inventors expressly elect, as their own lexicographers, to use only the plain and ordinary meaning of terms in the specification and claims unless they clearly state otherwise and then further, expressly set forth the “special” definition of that term and explain how it differs from the plain and ordinary meaning. Absent such clear statements of intent to apply a “special” definition, it is the inventors' intent and desire that the simple, plain and ordinary meaning to the terms be applied to the interpretation of the specification and claims.

The inventors are also aware of the normal precepts of English grammar. Thus, if a noun, term, or phrase is intended to be further characterized, specified, or narrowed in some way, then such noun, term, or phrase will expressly include additional adjectives, descriptive terms, or other modifiers in accordance with the normal precepts of English grammar. Absent the use of such adjectives, descriptive terms, or modifiers, it is the intent that such nouns, terms, or phrases be given their plain, and ordinary English meaning to those skilled in the applicable arts as set forth above.

Further, the inventors are fully informed of the standards and application of the special provisions of 35 U.S.C. § 112(f). Thus, the use of the words “function,” “means” or “step” in the Detailed Description or Description of the Drawings or claims is not intended to somehow indicate a desire to invoke the special provisions of 35 U.S.C. § 112(f), to define the invention. To the contrary, if the provisions of 35 U.S.C. § 112(f) are sought to be invoked to define the inventions, the claims will specifically and expressly state the exact phrases “means for” or “step for”, and will also recite the word “function” (i.e., will state “means for performing the function of [insert function]”), without also reciting in such phrases any structure, material or act in support of the function. Thus, even when the claims recite a “means for performing the function of . . . ” or “step for performing the function of . . . ,” if the claims also recite any structure, material or acts in support of that means or step, or that perform the recited function, then it is the clear intention of the inventors not to invoke the provisions of 35 U.S.C. § 112(f). Moreover, even if the provisions of 35 U.S.C. § 112(f) are invoked to define the claimed aspects, it is intended that these aspects not be limited only to the specific structure, material or acts that are described in the preferred embodiments, but in addition, include any and all structures, materials or acts that perform the claimed function as described in alternative embodiments or forms of the disclosure, or that are well known present or later-developed, equivalent structures, material or acts for performing the claimed function.

The foregoing and other aspects, features, and advantages will be apparent to those artisans of ordinary skill in the art from the DESCRIPTION and DRAWINGS, and from the CLAIMS.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure will hereinafter be described in conjunction with the appended drawings, where like designations denote like elements, and:

FIGS. 1A-1C show various views of a composite thermal dissipator comprising a PDMS composite material;

FIG. 2 shows a schematic view of a method for fabricating a composite thermal dissipator comprising the PDMS composite material;

FIGS. 3A-3C show various properties of the PDMS composite material;

FIG. 4A shows the steady-state temperature of materials under different heating loads;

FIG. 4B shows the calculated net radiative heat flux at different temperatures;

FIGS. 5A-5D show various properties of the PDMS composite thermal dissipator;

FIGS. 6A-6D show various properties of the PDMS composite thermal dissipator compared with an aluminum dissipator;

FIG. 7 shows a schematic cross-sectional view of a super-Planckian near-field thermal dissipator; and

FIGS. 8A-8D show the near-field radiative heat flux between emitter/receiver pairs having different thicknesses.

DETAILED DESCRIPTION

This disclosure, its aspects and implementations, are not limited to the specific material types, components, methods, or other examples disclosed herein. Many additional material types, components, methods, and procedures known in the art are contemplated for use with particular implementations from this disclosure. Accordingly, for example, although particular implementations are disclosed, such implementations and implementing components may comprise any components, models, types, materials, versions, quantities, and/or the like as is known in the art for such systems and implementing components, consistent with the intended operation.

The word “exemplary,” “example,” or various forms thereof are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “exemplary” or as an “example” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Furthermore, examples are provided solely for purposes of clarity and understanding and are not meant to limit or restrict the disclosed subject matter or relevant portions of this disclosure in any manner. It is to be appreciated that a myriad of additional or alternate examples of varying scope could have been presented, but have been omitted for purposes of brevity.

While this disclosure includes a number of embodiments in many different forms, there is shown in the drawings and will herein be described in detail particular embodiments with the understanding that the present disclosure is to be considered as an exemplification of the principles of the disclosed methods and systems, and is not intended to limit the broad aspect of the disclosed concepts to the embodiments illustrated.

High-performance electronic devices like central processing units (CPUs) and graphics processing units (GPUs) generate intensive heat. If not managed, this heat eventually leads to overheating problems and even system failure. Heat dissipation plays a crucial role in maintaining the reliability of electronic devices. However, along with an increasing demand for greater processing power, the form factors of these devices is becoming smaller and smaller due to the rising demands for mobile and wearable devices, making effective heat dissipation more challenging.

Traditionally, heat sinks have been the most used component for heat dissipation in electronic devices. They work by transferring the heat from the devices to the surrounding fluid medium, usually air or liquid coolants. Many efforts have been made to improve the performance of heat sinks. For example, optimizing the topology of heat sinks into tree-branch shapes significantly increased the Grashof number. Microchannels and nanofluids have been introduced to achieve extremely high heat transfer rates. Phase change materials have been employed in heat sinks as coolant due to their large heat of fusion. Carbon nanotubes have been employed as on-chip cooling fins, exhibiting cooling capacity for very high power density. Furthermore, metal foams offer advantages in thermal dissipation applications because of their low thermal resistance and lightweight properties. Working individually or filled in conventional fins, metal foams significantly enhance heat transfer performance.

Despite all the innovative approaches to improving performance, the working principle of a heat sink consists of two major processes: conducting heat out of the device and dissipating the heat to a medium. The conduction process requires high thermal conductivity of heat sink materials. Therefore, metals like aluminum and copper are commonly employed. The heat dissipation process is generally driven by either forced or natural convection. The nature of convection benefits from a larger surface area in contact with the cooling medium (e.g., air or coolant). As a result, most heat sinks have extended surfaces, or fins, to enhance the convectional heat transfer.

As another fundamental mechanism of heat transfer, thermal radiation is usually neglected when designing heat sinks with forced convection and small temperature difference above ambient conditions. This is because, in such cases, the convection is dominant. However, for natural-convection heat sinks, thermal radiation contributes 25-40% of the total heat transfer. This presents an opportunity for significantly improved heat transfer via radiative enhancement.

As previously mentioned, conducting heat out of a device requires high thermal conductivity. Metals are commonly employed for this reason. However, the thermal emittance of metals is usually very low, resulting in suppressed thermal radiation. Polymer materials, on the other hand, possess high emittance, which is essential for enhancing thermal emission. Furthermore, polymers are usually lightweight and manufacturing-friendly, able to be formed with complicated topologies. Yet despite all these attractive features, polymers are rarely used as heat sink or thermal dissipator materials, due to their low thermal conductivity.

Contemplated herein is a structured polydimethylsiloxane (PDMS) composite material for heat dissipation with enhanced thermal radiation, and methods for fabricating said composite. The contemplated structured polydimethylsiloxane composite (hereinafter “PDMS composite” or “composite”), is a novel material having enhanced thermal and radiative properties that make it ideal for use as a heat sink or thermal dissipator material.

Furthermore, contemplated herein is a composite thermal dissipator composed of this novel PDMS composite. According to various embodiments, the contemplated composite is a moldable composite of polydimethylsiloxane and metallic powder. This PDMS composite has properties that allow it to be formed into composite thermal dissipators with architectures very difficult and/or expensive to achieve using conventional heat sink materials. According to various embodiments, the contemplated composite can readily be fabricated into various shapes and sizes, such as high surface area fins.

Advantageously, the PDMS polymer enhances heat emissivity well beyond that of conventional metallic materials, and the copper enhances the thermal conductivity over conventional polymers used in heat transfer applications. Furthermore, due to the polymer host material, the composite can be formed into various shapes using a wax-mold method at near room temperature, as will be discussed below.

The contemplated PDMS composite outperforms traditional heat sink materials. In a specific embodiment, the thermal conductivity of the composite was enhanced by roughly 500%, rising from the 0.18 W/m·K of pure PDMS to 1.1 W/m·K. The thermal emissivity of this specific embodiment of the composite (0.8) was increased by about ten times, compared to commonly used aluminum (0.07, oxidized surface).

It should be noted that while the following disclosure contains a number of non-limiting examples of a novel composite material comprising PDMS and copper powder, other embodiments may employ different materials, such as different metals, or even additional metals. The methods and materials contemplated herein may be adapted for use with other polymers and/or metal powders, according to various embodiments. Those skilled in the art will recognize that heat sinks and thermal dissipators may be used in a range of contexts, and the adaptation of the contemplated composite, thermal dissipator, and methods for use with different materials may be advantageous when particular properties (e.g., mechanical, chemical, etc.) of the composite are prioritized.

Additionally, those skilled in the art will recognize that, while the contemplated composite material is being discussed in the non-limiting context of a heat sink for electronic devices, it may be applied in other settings or integrated into other heat dissipation applications with natural convection and moderate heating load.

FIGS. 1A-1C are various views of a non-limiting example of a composite thermal dissipator 100 comprising PDMS composite material 102. Specifically, FIG. 1A is a perspective view of a non-limiting example of a composite thermal dissipator 100 (hereinafter “composite dissipator 100”), FIG. 1B is a front view, and FIG. 1C is a cross-sectional view taken along line A-A of FIG. 1B.

As shown, the composite dissipator 100 may comprise a plurality of fins 106 to increase surface area and facilitate heat dissipation, as is known in the art. It should be noted that the non-limiting example shown in FIGS. 1A-1C is a rather simple architecture, and should not be considered to limit the architecture of other embodiments. In the context of the present description and the claims that follow, a fin is a protrusion through which heat may be dissipated. It may have any shape or size. In some embodiments, the fins 106 may be very simple, while in others the composite dissipator 100 may comprise fins 106 that are very complex. One of the advantages of the contemplated composite material 102 is that it makes possible dissipator designs that would otherwise be impractical (e.g., expensive or impossible to fabricate, etc.), as will be discussed further with respect to FIG. 2 , below.

In some embodiments, the composite dissipator 100 may be entirely made of the composite material 102. In other embodiments, the composite dissipator 100 may further comprise a substrate 104, such as an aluminum plate. The substrate 104 may facilitate the fabrication and installation processes, according to various embodiments.

According to various embodiments, the composite material 102 comprises a metallic powder mixed with PDMS. Polydimethylsiloxane (PDMS) is advantageous as a host material of the composite due to its versatility and low cost. PDMS has been widely investigated in applications of biomedicine, soft lithography, microfluidics, and radiative cooling. In other embodiments, other polymer materials may be used, as previously mentioned.

Due to its poor thermal conductivity, pure PDMS has not been used in many heat dissipation solutions, with the exception of microchannel heat sinks, in which the heat is removed by a liquid coolant flowing through PDMS channels. Contemplated herein is a composite material 102 having enhanced thermal conductivity and high thermal emittance that makes it ideal for heat dissipation applications having natural convection and moderate heating loads.

As will be discussed in greater detail below, the contemplated composite material 102 comprises metallic powder, which enhances the thermal conductivity of the composite material 102. In some embodiments, the metallic powder is copper powder. In other embodiments, other powdered metals may be used. In still other embodiments, more than one type of powdered metal may be used in creating the composite material 102.

One of the advantages of the contemplated composite material 102 over conventional materials is that it can employ fabrication methods otherwise not possible, methods that can produce very delicate/thin features such as fins 106. As is known in the art, one measure of a heat sink architecture, specifically a fin 106, is the perimeter to cross-sectional area, where the perimeter 108 is measured at the same point the cross-sectional area 110 is determined, as shown in FIG. 1 c . According to various embodiments, the contemplated composite dissipator 100 can have fins 106 with high perimeter to cross-sectional area ratios.

As a specific example, in one embodiment, a ratio of 100 m⁻¹ has been observed. In another embodiment, a ratio of 200 m⁻¹ was achieved. In still another embodiment, a ratio of 400 m⁻¹ was achieved using a sacrificial wax mold, as will be discussed below. Other embodiments were able to achieve ratios between 200 m⁻¹ and 400 m⁻¹. Still other embodiments were able to achieve ratios above 400 m⁻¹.

FIG. 2 is a schematic view of a method for fabricating a composite thermal dissipator 100 comprising the PDMS composite material 102. First, a powdered metal 200 is mixed with liquid polydimethylsiloxane (PDMS) 204 to form a liquid mixture 206. See ‘circle 1’.

According to various embodiments, PDMS is prepared from a two-part kit (e.g., Sylgard 184 from Dow Inc., etc.) having a base and a cure agent, which are mixed together at a weight ratio of 10:1. Cured, pure PDMS elastomer typically shows a thermal conductivity of ˜0.2 W/m·K, which is too low for heat sink materials. According to various embodiments, the thermal conductivity is enhanced by adding highly conductive materials, such as metals, carbon black, carbon nanotubes, graphene foam, aluminum nitride, and the like. For example, in some embodiments, copper powder 202 is added to liquid PDMS 204. Copper powder 202 is advantageous due to its low cost and high thermal conductivity (˜400 W/m·K for bulk copper).

As a specific example, in one embodiment, copper powder 202 having a particle size less than 75 μm (e.g., Product #207780 from Sigma-Aldrich Inc., etc.) is directly added into the PDMS liquid 204, as schematically shown in ‘circle 1’, and stirred using a glass rod.

According to various embodiments, the gel like PDMS/Cu liquid mixture 206 is then transferred into a vacuum chamber to remove air bubbles. The bubble-free mixture 206 is then cured on a hot plate at 150° C. for 10 minutes.

According to various embodiments, the ratio of powdered metal 200 to PDMS is between 3.7 and 4. As will be discussed in greater detail below, the addition of metal powder 200 to the PDMS raises the materials thermal conductivity, which continues to rise as the weight ratio of metal to PDMS increases. However, there is a point where the structural consequences outweigh the thermal benefits. For example, in one embodiment, the thermal conductivity of the composite 102 reaches 1.1 W/m·K with a Cu weight ratio of 3.75, which is a 500% enhancement comparing to the pure PDMS. However, elevating the weight ratio higher than 4 often makes the PDMS/metal mixture 206 extremely viscous and difficult to pour into a mold for shaping.

Next, the liquid mixture 206 of liquid PDMS 204 and metal powder 200, which now may be gel-like, is slowly poured into a mold 208, the mold 208 shaped to be complementary to the composite thermal dissipator 100. See ‘circle 2’. In the context of the present description and the claims that follow, a mold 208 that is shaped to be complementary to the composite thermal dissipator 100 means a hollow container that has been topographically patterned to yield the desired composite thermal dissipator 100 when used to give shape to the liquid mixture 206 that subsequently hardens.

The performance of a heat sink depends not only on the materials but also on the geometry. Conventional molding processes for PDMS, such as those used in soft lithography, typically involve PDMS liquid 204 being poured into a prefabricated mold. To facilitate the subsequent demolding process, the mold needs to be surface modified to prevent solidified PDMS from sticking to the mold. The modification process requires extreme caution because toxic and corrosive reagents are used. Still more problematic is the fact that even a modified mold cannot produce patterns with a high perimeter to cross-sectional area ratio, as the PDMS composite may be torn apart when peeled from the mold. As a specific example, a perimeter to cross-sectional area ratio of 100 m⁻¹ did not survive the removal of a surface modified mold. The perimeter to cross-sectional area ratio needs to be high for heat sinks; thin and tall fins are preferred in heat sinks, to extend the surface area. Contemplated herein is a method that overcomes these demolding problems.

According to various embodiments, a sacrificial wax mold 210 is used, making it feasible to fabricate slim fins 106 or other features that would be torn apart using traditional PDMS molding methods. The use of a sacrificial wax mold 210, with wax 212 shaped to be complementary to the composite thermal dissipator 100, makes it possible to achieve perimeter 108 to cross-sectional area 110 ratios not feasible with surface modified molds. As a specific example, in one embodiment, a ratio of 100 m⁻¹ was achieved. In another embodiment, a ratio of 200 m⁻¹ was achieved. In still another embodiment, a ratio of 400 m⁻¹ was achieved using a sacrificial wax mold. Other embodiments were able to achieve ratios between 200 m⁻¹ and 400 m⁻¹. Still other embodiments were able to achieve ratios above 400 m⁻¹.

Another advantage that sacrificial wax molds 210 have over conventional PDMS molding methods is that the mold 208 is inexpensive, and easy to shape. According to various embodiments, a wax block (e.g., paraffin wax, etc.) may be machined to form patterns complementary to those of the designed fins 106. In some embodiments, this machining may be performed using a drill. Those skilled in the art will recognize that other methods and/or tools for preparing a wax mold 210 may be adapted for use in molding the contemplated composite. For example, in some embodiments, complicated patterns can be realized using 3D-printed wax molds.

In some embodiments, after the liquid PDMS/metal mixture 206 has been poured into the mold 208, the mold 208 may be covered by a substrate 104 (e.g., an aluminum plate, etc.) such that the substrate 104 is in contact with the liquid mixture 206. See ‘circle 3’. In other embodiments, the composite thermal dissipator 100 may be molded without the addition of a substrate 104.

Next, the liquid mixture 206 is cured within the mold 208. See ‘circle 4’. In some embodiments, the wax 212 has a melting point of around 40° C. This means the PDMS/metal mixture 206 should not be cured at elevated temperatures, but instead at roughly room temperature. As a specific example, in one embodiment, the liquid mixture 206 is cured for 24 hours. In other embodiments, the mixture 206 may be cured at elevated temperatures.

Finally, the composite thermal dissipator 100 is removed from the mold 208. See ‘circle 5’. According to various embodiments, the solidified PDMS/metal composite 102 may be demolded from a sacrificial wax mold 210 by melting the wax 212. As a specific example, in one embodiment, the wax 212 is melted away on a hot plate at 100° C., resulting in PDMS/Cu fins 106 coupled to a substrate 104.

FIGS. 3A through 3 c show various properties of specific but non-limiting examples of the contemplated composite material 102. Specifically, FIG. 3A shows the thermal conductivity of the composite 102 with different copper to PDMS weight ratios. FIG. 3 b shows spectral emissivity and FIG. 3 c shows total emissivity of those same embodiments.

The thermal conductivities, k, of FIG. 3A were characterized using the well-established hot disk transient plane source (TPS) method. In a specific embodiment, and using a commercial apparatus (e.g., TPS 2500S from Thermtest Inc., etc.), two identical cylinder samples with a diameter of 25 mm and a thickness of 10 mm were attached to each side of a film sensor of a thickness of 100 μm. A current is applied to the sensor to generate heat, and the sensor temperature as a function of time is monitored by a high-precision multimeter. The thermal conductivity and thermal diffusivity of the test sample can be determined automatically through the relation between the sensor temperature and time.

As shown, the thermal conductivity of pure PDMS, without copper powder 202, is 0.18 W/m·K. With the addition of Cu powder 202, the thermal conductivity of the composite rises as the weight ratio of Cu to PDMS increases. As a specific example, in one embodiment, the thermal conductivity of the composite reaches 1.1 W/m·K with a Cu weight ratio of 3.75, which is a 500% enhancement comparing to the pure PDMS. In other embodiments, thermal conductivity can be further increased with more Cu powder 202 added, however, elevating the weight ratio higher than 4 often makes the PDMS/Cu mixture 206 extremely viscous and difficult to pour into a mold for shaping.

Radiation properties may be measured through a Fourier-transform infrared spectrometer (e.g., Nicolet iS50 from Thermo Fisher Scientific Inc., etc.) equipped with a gold integrating sphere (e.g., Mid-IR IntegratIR from PIKE Technologies, etc.). spectral emissivity, ε_(λ), of 1-mm-thick PDMS or PDMS/Cu composite 102 on aluminum sheets, as well as a bare aluminum sheet are compared in FIG. 3 b . An aluminum sheet, like most metals, shows low emissivity in the infrared regime, while PDMS has high emissivity close to unity. The addition of Cu powder 202 decreases spectral emissivity. It should be noted that the decrease of ε_(λ) occurs mainly in the wavelength range of 2-8 μm, while ε_(λ) in the wavelength longer than 8 μm is not significantly affected by copper inclusions.

As shown, the spectral emissivity exhibits little changes when the Cu weight ratio is larger than 2. The change in radiation properties can be explained through effective medium theory (EMT). In this theory, the property of the composite 102 is determined by the matrix medium (PDMS in this case), inclusion (Cu powder 202 in this case), and the volume fraction of the inclusion. When the weight ratio of Cu is 3.75, the volume fraction of Cu is only 0.29, which is still small compared with PDMS. Therefore, the radiation property of the composite is not affected too much by the addition of Cu powder 202, retaining relatively high emissivity.

Based on the spectral emissivity, total emissivity was calculated through

${\varepsilon(T)} = \frac{\int{{\varepsilon_{\lambda}(\lambda)}{E_{\lambda,b}\left( {\lambda,T} \right)}d\lambda}}{\int{{E_{\lambda,b}\left( {\lambda,T} \right)}d\lambda}}$

wnere E_(λ,b) is the spectral emissive power of a blackbody at temperature T given by Planck's law. The temperature-dependent total emissivity of the samples is compared in FIG. 3 c . Pure PDMS holds the highest total emissivity, which is around 0.97, and aluminum sheet has the lowest emissivity of 0.07. Unlike the dramatic drop in the spectral emissivity at λ of 2-8 μm, the total emissivity of PDMS/Cu composite slightly decreases to 0.85 with Cu weight ratio of 1 compared to that of pure PDMS, due to the high spectral emissivity at λ>8 μm of PDMS/Cu. The total emissivity of PDMS/Cu remains around 0.8 even when Cu weight ratio increases to 3.75, which is almost ten times higher than that of the bare aluminum sheet. High total emissivity implies effective radiation transfer when the proposed composite is employed for heat dissipation applications, as radiative power is linear to the total emissivity.

FIGS. 4A and 4B show the results of various performance tests performed on specific but non-limiting examples of the contemplated composite material 102. Specifically, FIG. 4A shows the steady-state temperature of samples at different heating loads. FIG. 4B shows calculated net radiative heat flux at different sample temperatures. It should be noted that markers are used for experimental data, and dashed lines represent simulated results from ANSYS.

A series of thermal tests were conducted to directly demonstrate the performance of various embodiments of the contemplated PDMS/Cu composite, in which the Cu weight ratio was fixed at 3. First, the effect of the enhanced emissivity is examined by comparing three 1.5-inch-by-1.5-inch (38×38 mm²) sheet samples: a bare aluminum sheet, an aluminum sheet with a film of pure PDMS, and an aluminum sheet with a PDMS/Cu film.

The steady-state temperatures under various heating loads are plotted as markers in FIG. 4A. The temperatures of the bare aluminum sheet are the highest, while those of the PDMS film is the lowest, showing a 10° C. temperature difference under a heating load of 1000 W/m². The temperatures of the PDMS/Cu film are lower than those of the aluminum sheet and slightly higher than those of pure PDMS.

The experimental results show that the heat dissipation performances of the PDMS and PDMS/Cu film samples are close to each other and much better than that of the aluminum sheet. The trend in cooling performance is consistent with that in the total emissivity: £ of PDMS and PDMS/Cu is close to each other and much higher than that of Al.

The temperatures were simulated in ANSYS thermal solver and are shown as dashed lines in FIG. 4A. Using the simulation tool, the net radiative heat flux leaving the sample surface can be extracted. As compared in FIG. 4B, the radiative heat flux of the aluminum sheet is the lowest among the samples, which is the result of low emissivity of Al. The radiative heat flux from the PDMS/Cu sample is much higher than that of Al, thanks to the enhanced emissivity of PDMS/Cu compared with Al. With the emissivity close to unity, the PDMS sample has slightly higher radiative heat flux than that of PDMS/Cu. These results demonstrate the positive effect of the emissivity enhancement of PDMS/Cu composite 102 on heat dissipation.

FIGS. 5A through 5D show the results of various performance tests for finned thermal dissipators, including a specific but non-limiting example of the contemplated composite thermal dissipator 100. Specifically, FIG. 5A shows the steady-state temperature of exemplary thermal dissipators at different input powers. FIG. 5B shows the calculated convective heat flux at different sample temperatures. FIGS. 5C and 5D show a schematic representation illustrating the temperature distributions at a power input of 1000 W/m² for the PDMS dissipator and composite dissipator 100, respectively. Again, it should be noted that experimental data is represented by markers, and simulated results from ANSYS are plotted as dashed lines.

To demonstrate the influence of thermal conductivity, non-limiting examples of heat sinks were fabricated following the fabrication method previously discussed, and depicted in FIG. 2 . Specifically, rectangle fins 106 were chosen as the heat sink, and the height h, thickness t, length L, and distance d are 0.3 inch (0.76 cm), 0.15 inch (0.38 cm), 1.5 inch (3.8 cm), and 0.15 inch (0.38 cm), respectively. A total number of five fins 106 were fabricated on a 1.5-inch by 1.5-inch aluminum sheet. The fins 106 are made of either pure PDMS or PDMS/Cu composite 102, aiming to exclude the effect of the radiation as a result of similar emissivity of these two materials. Measured steady-state temperatures of substrates 104 (i.e., the aluminum sheet on which the fins 106 were attached), are shown in FIG. 5A as markers, where results of the PDMS film sample are also given. The difference between PDMS film and PDMS fins 106 presents the effect of extending surfaces, which is the basic function of fins 106.

As mentioned before, the fins 106 facilitate heat dissipation by conducting heat from the substrate 104 to the extended surface of the fin 106 and dumping the heat to the surrounding medium. With these extended surfaces, the temperatures of PDMS fins are lower than those of PDMS film, although the temperature difference is quite small. The small difference is because the heat cannot be conducted to the extended surfaces effectively due to the low thermal conductivity of pure PDMS, which has been improved by introducing copper powders 202 to the contemplated composite material 102. The convective heat flux from the fin surfaces to ambient air, which was extracted in ANSYS simulations, is provided in FIG. 5B. As shown, the convective heat flux of the PDMS fins is larger than that of the PDMS film, explaining the better heat dissipation performance of fins.

The performance is further improved when the fin material is changed from PDMS to PDMS/Cu composite 102, as shown by the lowest temperatures of PDMS/Cu fins in FIG. 5A. Due to the enhanced thermal conductivity, the heat of the substrate 104 (i.e., the aluminum sheet), can be easily conducted to the extended surfaces of the fins 106, which is visualized in FIGS. 5C and 5D using the temperature distributions from simulation. As a result of enhanced thermal conductivity, the distribution of the composite thermal dissipator 100 is more uniform than that of the pure PDMS. With the heating load of 1000 W/m², the lowest temperature of the PDMS/Cu fins, which occurs at a fin tip, is 55.3° C., 12.7° C. higher than that of the PDMS fins. Higher surface temperature means more heat transferred to air via convection (further confirmed by the convective heat flux in FIG. 5B) and more heat conducted from the base. As a result, the base temperature of PDMS/Cu fins is nearly 8° C. lower than the PDMS counterpart, validating the positive effect of thermal conductivity enhancement.

FIGS. 6A through 6 c show the results of additional performance tests. Specifically, these tests are comparing a specific but non-limiting example of the contemplated composite thermal dissipator 100 with Al fins. FIG. 6A shows the steady-state temperature of the samples at different input powers. Again, experimental data is represented as markers, while simulated results from ANSYS are plotted as dashed lines. FIG. 6B shows calculated heat fluxes at different sample temperatures, while FIGS. 6C and 6D shows the temperature distributions at a power input of 1000 W/m² for the contemplated composite thermal dissipator 100 and an aluminum dissipator.

As shown, the PDMS/Cu finned thermal dissipator 100 is directly compared with aluminum fins. The aluminum fins have the same geometry as the PDMS/Cu fins, and their heat dissipation performance is shown in FIG. 6A in terms of steady-state temperatures. The base temperature of the PDMS/Cu fins is lower than that of the aluminum fins, indicating a better heat dissipation performance of the PDMS/Cu fins over the aluminum counterpart.

The same geometry of these two samples means that the differences in convection coefficient and ambient can be excluded, and the performance difference is exclusively due to the materials. Aluminum, as a common material for heat sinks, is commonly used in this context since it is light weight and has high thermal conductivity, which is nearly 200 W/m·K and two orders of magnitude higher than the PDMS/Cu composite. As discussed above, high thermal conductivity boosts the heat transfer from the base to the extended surfaces and thus enhances the heat convection, which is confirmed by the larger convective heat flux of the aluminum fins than that of the PDMS/Cu samples in FIG. 6B.

The influence of the thermal conductivity can be visualized by plotting the temperature fields of the samples and those under the heating load of 1000 W/m², as shown in FIGS. 6C and 6D. The temperature distribution of the aluminum sample is quite uniform due to the high thermal conductivity, with a temperature difference between the base and fin tip of just 0.2° C. The temperature at the fin tip is 11° C. higher than the tip temperature of the PDMS/Cu fins, verifying the larger convective heat flux of the aluminum sample.

However, convection is not the only mechanism that is related to heat dissipation; radiation also exerts a strong influence. The high emissivity of PDMS/Cu composites 102 facilitates the radiation heat transfer, resulting in larger emissive heat flux than Al, which has very low emissivity, as seen in FIG. 6B. The total heat flux leaving the PDMS/Cu sample is higher than that leaving the aluminum sample, resulting in a lower substrate 104 temperature of the PDMS/Cu sample. For example, the results in FIG. 6 c show that the base (i.e., substrate 104) temperature of the PDMS/Cu fins is 2.5° C. lower than that of the aluminum sample under a heating load of 1000 W/m². Note that the base temperature of the pure PDMS sample, whose thermal emissivity is close to unity, under the same condition is 5.4° C. higher than that of the aluminum sample, which emphasizes that the best heat dissipation performance of the PDMS/Cu fins is a result of the improvement on both thermal conductivity and emissivity.

Some embodiments of the composite material 102 may not be appropriate to replace metals in load-intensive applications because radiation is almost negligible compared with convection. In such applications, the convection is usually forced convection and involves liquid coolant. However, in the case of free-air convection for moderate heating loads, various embodiments of the contemplated composite 102 surpass metals due to the radiation reinforcement. Furthermore, the contemplated PDMS composite 102 can be easily shaped at low temperatures (<100° C.). As a result, some embodiments of the PDMS/Cu composite 102 may be used as a prototype material for metallic heat sinks in the designing stage. Furthermore, using 3D-printed wax molds, the composite 102 can be fabricated into composite thermal dissipators 100 with a complex topology that is high-performance but difficult for conventional metal fabrication.

In the context of microelectronics, dealing with unwanted heat is further complicated by size constraints. Modern microelectronics continue to increase in power while also decreasing in size, thanks to advancements in fabrication technologies, materials, and device architectures. As a result, heat dissipation has become a significant bottleneck for microelectronics. An increasing amount of heat needs to be transferred without sacrificing the small size of the device. Previous attempts at solving this problem have not recognized radiation as a viable means for dissipating heat in these devices, mainly due to the limitation of dealing in the far field.

Photon tunneling in the near-field can enhance radiative heat transfer to overcome the blackbody limit governed by Planck's law when the vacuum gap between two radiating media is much less than the characteristic thermal wavelength. Potential applications of near-field radiation (NFR) include, but are not limited to, near-field thermopower generation (e.g., thermophotovoltaics, etc.), noncontact heat control (e.g., thermal rectification, etc.), and radiative refrigeration.

Previous attempts to harness near-field radiation for super-Planckian radiative heat have relied on polar materials, or formed the gap between a microsphere and a surface, greatly limiting the total radiative heat transfer. Achieving nanometer gaps and parallelism across mesoscale lateral size of plate-plate configurations has been a major challenge. Previous methods of creating the vacuum gap include the formation of low-density pillars, a solution that would be expensive and difficult to scale up for implementation outside a laboratory setting.

Some prior efforts to enhance near-field radiation have employed various materials, such as glass and bare silicon. Metals, on the other hand, are much less studied for near-field thermal radiation. Metals are widely used in microelectronics (e.g., electrodes, conducting pads, etc.). Metals are known to have plasma frequencies typically in the ultraviolet to the visible wavelength ranges; therefore, coupled surface plasmon polaritons cannot occur in the infrared for significant near-field enhancement around room temperature. In addition, metals are normally known as bad thermal emitters in the far-field due to their very low emissivity, typically just a few percent.

Contemplated herein is a super-Planckian near-field thermal dissipator and method for producing the same. This super-Planckian near-field thermal dissipator (hereinafter “near-field thermal dissipator”) makes use of two metallic (e.g., aluminum, etc.), planar surfaces that have been brought very close together to form a vacuum gap. In some embodiments, radiative heat transfer has been shown (theoretically and experimentally) to be enhanced roughly 400 times, compared to conventional far-field transfer.

As will be discussed in greater detail below, in one embodiment, an aluminum thin-film emitter with the same thickness as a receiver is separated from the receiver by polystyrene nanoparticles, under a total applied force of 30 mN, creating a vacuum gap around 200 nm. The vacuum gap is maintained by a distribution of nanoparticles. Advantageous over other methods for creating and maintaining a vacuum gap, the use of nanoparticles results in a gap size that is easy to produce consistently, and is scalable.

Additionally, unlike conventional attempts at near-field thermal dissipators, the contemplated near-field thermal dissipator makes use of scalable and tunable fabrication methods. The vacuum gap where heat is transferred between metallic surfaces can be controlled using polymeric spheres, such as polystyrene nanoparticles, to maintain a uniform distance leading to uniform performance. Metal layers can be nanometrically tuned to control the thin-film resonant effects to further enhance heat transfer. The design thicknesses and gaps can be readily controlled and tuned based on the application.

Near-field and thin-film effects work together to provide enhanced radiative heat transfer. The design augments contributions from non-resonant coupling within the subwavelength vacuum gap and from resonant coupling within the nanometric aluminum thin films with s-polarized waves.

According to various embodiments, nanometer-level control of thickness, materials of construction, and subwavelength vacuum gap spacing in the multilayered device greatly enhances radiative heat transfer, referred to as super-Planckian heat transfer, between metallic surfaces. In particular, nanometric control of the aluminum thicknesses within the emitter and receiver and the gap distance between the aluminum layers results in a radiative heat flux of about 6.4 times over the blackbody limit and 420 times over that of the far-field radiative heat transfer at a temperature difference of 65K with a receiver at room temperature.

FIG. 7 is a schematic cross-sectional view of a non-limiting example of a super-Planckian near-field thermal dissipator 700. As shown, the near-field thermal dissipator 700 comprises a metallic emitter 704 and a metallic receiver 702, separated by a vacuum gap 716. According to various embodiments, the vacuum gap 716 is maintained by nanoparticles 714.

As shown, the receiver 702 comprises a first metallic thin-film 706, and the emitter 704 comprises a second metallic thin-film 708. In some embodiments, the first metallic film 706 may be composed of the same material as the second metallic film 708, while in other embodiments they may be composed of different materials. In some embodiments, one or both of these films may be composed of aluminum. In other embodiments, these thin films may be composed of other metals, such as gold.

Additionally, as shown, in some embodiments, one or both of the thin films may be deposed on a substrate material (i.e., first substrate material 710 and second substrate material 712), such as lightly-doped silicon or other materials known in the art. In some embodiments, the first substrate material 710 may be the same as the second substrate material 712, while in others they may be different materials.

In some embodiments, the emitter 704 and receiver 702 are millimeter-scale. As a specific example, in one embodiment, the near-field thermal dissipator 700 may be 5 mm×5 mm, a common size for microelectronics chips. Other embodiments may comprise a larger emitter 704 and receiver 702, while others may be smaller.

As mentioned above, the near-field thermal dissipator 700 enhances thermal transfer through near-field and thin-film effects. According to various embodiments, the thickness of the first metallic film 706 that forms the receiver 702 and the second metallic film 708 that forms the emitter 704 is nanoscale. As a specific, non-limiting example, in one embodiment, these films may be 79 nm thick. In another embodiment, these films may be as thin as 13 nm. In other embodiments, the films may be even thinner. Theoretical calculations have predicted even better near-field radiative heat flux with thinner metallic thin-films.

Forming and maintaining a subwavelength vacuum gap 716 (e.g., 200 nm, etc.) in a manner that is scalable, practical, and yields consistent results is an engineering challenge that previous efforts at a near-field thermal dissipator have failed to overcome. Advantageously, the contemplated near-field thermal dissipator 700 makes use of nanoparticles 714 dispersed on the metallic film surface to form and maintain the vacuum gap 716 effectively. The fabrication process, which can be done in a laboratory environment rather than a nanoscale fabrication environment, will be discussed further below.

In some embodiments, the nanoparticles 714 are composed of polystyrene. Polystyrene is advantageous due to its low thermal conductivity of 0.18 m⁻¹ K⁻¹. In other embodiments, the nanoparticles 714 may be composed of other materials known in the art that have low thermal conductivity and are able to form particles of the desired size with sufficient consistency as to maintain a uniform and predictable gap size.

As a specific non-limiting example, in one embodiment, the near-field thermal dissipator 700 comprises 13-nm-thick aluminum films (i.e., first metallic film 706 and second metallic film 708) deposed on lightly doped silicon (i.e., first substrate material 710 and second substrate material 712) and separated by a vacuum gap 716 distance of 215 nm formed with polystyrene nanoparticles 714 having an average diameter of roughly 200 nm. This particular embodiment results in an enhancement of 6.4 times over the blackbody limit and 420 times over the limit of the far-field radiative heat transfer between bulk aluminum at a temperature difference of 65 K, with the receiver 702 at room temperature. The mechanisms of the heat flux enhancement come from augmented contributions from non-resonant coupling within the subwavelength vacuum gap 716 (i.e., near-field effect) and from resonant coupling within the nanometric metallic thin film (i.e., thin-film effect) with s-polarized waves.

According to various embodiments, the vacuum 720 within the near-field thermal dissipator's gap 716 may be maintained by a housing 718 that encloses the near-field thermal dissipator 700, as is known in the art (e.g., packaging for organic solar cells, etc.). In some embodiments, the vacuum 720 that is maintained may be as low as 1 Pa. As an option, in some embodiments, the near-field thermal dissipator 700 may be packaged together with the target of thermal control (i.e., microelectronic, etc.) while in a low vacuum environment.

According to various embodiments, the emitter 704 and receiver 702 each comprise a thin film of metal (i.e., first metallic film 706 and second metallic film 708) deposed on a substrate (i.e., first substrate material 710 and second substrate material 712). As a specific example, in one embodiment, aluminum thin films are coated on 5×5 mm² lightly doped silicon chips (e.g., from Ted Pella Inc., 1-30 Ωcm resistivity, 500±30 μm thickness) via an electron beam evaporation method with the deposition rate of 0.5 Å/s. This coating is performed after a cleaning process using isopropanol alcohol, de-ionized water, and oxygen plasma. Other embodiments may employ other film deposition methods known in the art.

Next, nanoparticles 714 are placed on the surface of either the receiver 702 or emitter 704, in preparation for the creation of the vacuum gap 716. As a specific non-limiting example, in one embodiment, polystyrene particles 714 with an average particle diameter of 198 nm and standard deviation of 6 nm (e.g., Sigma Aldrich, 690575ML-F) are used. Said particle 714 is originally in a solution of deionized water at a concentration of 2.4×10¹³ particles/mL. A two-step dilution process is performed by first mixing 0.02 mL of the initial particle suspension and 100 mL of deionized water and then mixing 0.1 mL of the intermediate suspension and 61 mL of deionized water for the second dilution. Both dilution processes are done with an Elmasonic Bath Sonicator to prevent possible aggregation and obtain uniform suspension of particles within the solutions. As a result, the particle concentration is reduced to 7.8×10⁶ particle/mL to create the desired vacuum gap 716 with minimized conduction heat transfer. In other embodiments, other concentrations and methods known in the art may be employed.

According to various embodiments, the nanoparticle solution is deposited on one of the emitter 704 and the receiver 702. As a specific example, in one embodiment, 0.02 mL of the finally diluted solution with approximately 1.56×10⁵ polystyrene nanoparticles 714 is deposited via a syringe onto the receiver 702 surface, which is then placed on a hotplate to remove the water upon heating. In some embodiments, this surface is then carefully inspected under an optical microscope for large particle aggregation and dust particles, which can adversely affect the creation of nanometric vacuum gap 716 distance.

Finally, the other thin film is placed on top of the nanoparticles 714, and then placed in a vacuum environment, creating a vacuum gap 716 between the receiver 702 and emitter 704. In some embodiments, this vacuum 720 may be maintained by enclosing the near-field thermal dissipator 700 within a housing 718.

FIG. 8 shows the near-field radiative heat flux between aluminum thin films (i.e., receiver 702 and emitter 704 of a non-limiting example of the contemplated near-field thermal dissipator 700) of four different thicknesses, as a function of temperature difference T. Specifically, a comparison between the measured near-field radiative heat flux and the theoretical calculations at a fitted vacuum gap 716 of d=215 nm is shown in FIGS. 8A-8D for Al thin films with different thicknesses: (a) 13±2 nm, (b) 24±3 nm, (c) 40±3 nm, and (d) 79±3 nm. The shaded area displays the calculated near-field radiative flux considering the uncertainty of the vacuum gap 716 distance, 215 (+55,−50) nm obtained from four near-field radiation measurements between bare Si chips, whereas solid black lines denote the near-field radiative heat fluxes at the average vacuum gap 716 distance of d=215 nm. The measured near-field radiative heat fluxes q_(NFR,exp), symbolized by the markers with error bars as combined uncertainties U_(c), overlap with theoretical predictions considering upper and lower bounds due to the uncertainty of the fitted vacuum gap 716, indicating good agreement. There is slight difference, in particular, for 13-nm Al thin film, which is mainly because of optical constants of Al used for modeling and experimental uncertainties of vacuum gap 716 and heat flux measurements.

In the insets of FIGS. 8A-8D, the total radiative heat flux of the Al thin films at a vacuum gap 716 distance of 215 nm is compared with the blackbody limit and far-field radiation of bulk aluminum surfaces. The theoretical results indicate that the total radiative heat flux between the 13-nm Al thin-film samples separated by a vacuum gap 716 of 215 nm is ˜5224 W/m² for the temperature difference ΔT=65 K, indicating an improvement about 10 times over the blackbody limit and 650 times compared to the far-field radiation of the bulk aluminum sample. The near-field radiative heat flux for thicker Al samples was calculated to be 3943 W/m², 2846 W/m², and 1901 W/m² for 24, 40, and 79-nm-thick Al films, respectively, under the same temperature difference of 65 K. As shown, the near-field radiative heat flux decreases monotonically with increasing aluminum thickness.

Additional results suggest that the near-field enhancement over the blackbody limit could potentially reach 42 times with 15-nm-thick Al at a vacuum gap 716 of 100 nm, or even 123 times with 20-nm-thick Al at a vacuum gap 716 of 50 nm. When compared to the far-field radiation with bulk Al, the near-field and thin-film effects could enhance the radiation heat flux up to 2750 times with 15-nm-thick Al at d=100 nm or 8060 times with 20-nm-thick Al at d=50 nm.

It will be understood that implementations are not limited to the specific components disclosed herein, as virtually any components consistent with the intended operation of a structured polydimethylsiloxane (PDMS) composite for heat dissipation, a composite thermal dissipator, and method for fabricating the same may be utilized. Accordingly, for example, although particular composite materials may be disclosed, such components may comprise any shape, size, style, type, model, version, class, grade, measurement, concentration, material, weight, quantity, and/or the like consistent with the intended operation of a structured PDMS composite for heat dissipation, a composite thermal dissipator, and method for fabricating the same may be used. In places where the description above refers to particular implementations a structured PDMS composite for heat dissipation, a composite thermal dissipator, and method for fabricating the same, it should be readily apparent that a number of modifications may be made without departing from the spirit thereof and that these implementations may be applied to other heat dissipation composite materials and devices.

Furthermore, it will be understood that implementations are not limited to the specific components disclosed herein, as virtually any components consistent with the intended operation of a super-Planckian near-field thermal dissipator and/or method for producing the same may be utilized. Accordingly, for example, although particular super-Planckian near-field thermal dissipators and methods for producing the same may be disclosed, such components and steps may comprise any shape, size, style, type, model, version, class, grade, measurement, concentration, material, weight, quantity, and/or the like consistent with the intended operation of a super-Planckian near-field thermal dissipator may be used. In places where the description above refers to particular implementations of a super-Planckian near-field thermal dissipator and/or method for producing the same, it should be readily apparent that a number of modifications may be made without departing from the spirit thereof and that these implementations may be applied to other near-field thermal dissipators. 

What is claimed is:
 1. A method for fabricating a composite thermal dissipator, comprising: mixing a powdered copper into liquid polydimethylsiloxane (PDMS) to form a liquid mixture; pouring the liquid mixture into a sacrificial wax mold, the sacrificial wax mold comprising wax shaped to be complementary to the composite thermal dissipator; curing the liquid mixture within the sacrificial wax mold; and removing the composite thermal dissipator from the sacrificial wax mold by melting away the wax.
 2. The method of claim 1, further comprising: covering the sacrificial wax mold with a substrate such that the substrate is in contact with the liquid mixture; wherein the composite thermal dissipator comprises the substrate.
 3. The method of claim 1, wherein the powdered copper has a particle size of less than 75 μm.
 4. The method of claim 1, wherein the weight ratio of powdered copper to PDMS is between 3.7 and
 4. 5. The method of claim 1, wherein the composite thermal dissipator comprises a plurality of fins, each fin having a perimeter and a cross-sectional area, wherein the perimeter-to-cross-sectional-area ratio is at least 400 m⁻¹.
 6. A method for fabricating a composite thermal dissipator, comprising: mixing a powdered metal into liquid polydimethylsiloxane (PDMS) to form a liquid mixture; pouring the liquid mixture into a mold, the mold shaped to be complementary to the composite thermal dissipator; curing the liquid mixture within the mold; and removing the composite thermal dissipator from the mold.
 7. The method of claim 6: wherein the mold is a sacrificial wax mold comprising wax shaped to be complementary to the composite thermal dissipator; and wherein removing the composite thermal dissipator from the mold comprises melting away the wax of the sacrificial wax mold.
 8. The method of claim 6, further comprising: covering the mold with a substrate such that the substrate is in contact with the liquid mixture; wherein the composite thermal dissipator comprises the substrate.
 9. The method of claim 6, wherein the powdered metal is powdered copper.
 10. The method of claim 6, wherein the powdered metal has a particle size of less than 75 μm.
 11. The method of claim 6, wherein the weight ratio of powdered metal to PDMS is between 3.7 and
 4. 12. The method of claim 6, wherein the composite thermal dissipator comprises a plurality of fins, each fin having a perimeter and a cross-sectional area, wherein the perimeter-to-cross-sectional-area ratio is at least 400 m⁻¹.
 13. The method of claim 6, wherein the liquid mixture is cured within the mold at room temperature.
 14. A composite thermal dissipator, comprising a molded PDMS composite material composed of a powdered metal mixed with PDMS.
 15. The composite thermal dissipator of claim 14, further comprising a substrate coupled to the molded composite material.
 16. The composite thermal dissipator of claim 14, wherein the powdered metal is powdered copper.
 17. The composite thermal dissipator of claim 16, wherein the powdered metal has a particle size of less than 75 μm.
 18. The composite thermal dissipator of claim 17, wherein the weight ratio of powdered metal to PDMS is between 3.7 and
 4. 19. The composite thermal dissipator of claim 14, further comprising a plurality of fins, each fin having a perimeter and a cross-sectional area, wherein the perimeter-to-cross-sectional-area ratio is at least 400 m⁻¹. 